Question

question 10

simplify: \\(\sqrt{507w^{10}z^{13}}\\)

\\(\bigcirc\\) \\(13w^5z^6\sqrt{3z}\\)
\\(\bigcirc\\) \\(13w^{10}z^{12}\sqrt{3z}\\)
\\(\bigcirc\\) \\(w^{10}z^{12}\sqrt{507z}\\)
\\(\bigcirc\\) \\(w^5z^6\sqrt{507z}\\)

Explanation:

Factor the cube root expression

We simplify the cube root in Question 9:

$$ \sqrt[3]{54a^7b^{18}} $$

We find perfect cubes:

$$
LATEXBLOCK0
$$

Extract perfect cubes

Using Simplifying Radicals:

$$ \sqrt[3]{3^3 \cdot 2 \cdot (a^2)^3 \cdot a \cdot (b^6)^3} = 3a^2b^6\sqrt[3]{2a} $$

Factor the square root expression

We simplify the square root in Question 10:

$$ \sqrt{507w^{10}z^{13}} $$

Using Simplifying Square Roots with Variables:

$$
LATEXBLOCK1
$$

Extract perfect squares

We pull out the squared terms:

$$ \sqrt{13^2 \cdot 3 \cdot (w^5)^2 \cdot (z^6)^2 \cdot z} = 13w^5z^6\sqrt{3z} $$

Answer:

Question 9

Simplify: \(\sqrt[3]{54a^7b^{18}} =\) <blank>\(3a^2b^6\sqrt[3]{2a}\)</blank>

Question 10

• (A) \(13w^5z^6\sqrt{3z}\) (Correct answer)
• (B) \(13w^{10}z^{12}\sqrt{3z}\)
• (C) \(w^{10}z^{12}\sqrt{507z}\)
• (D) \(w^5z^6\sqrt{507z}\)